The meaning of "在留" in various phrases and sentences

在留期間の満了日（Expiration date of you staying）ex, 1st of September
2か月を経過（2 months elapsed from that）1st of September + 2 months = 1st of November
10日前（10 days before from that）1st of November - 10 days = 23rd of October
so, "在留期間の満了日から2ヶ月を経過する日の10日前" = 23rd of October
If you don't receive 通知書（Notice letter）until 23rd of October, please ask it to the authorities.